Memoization to Optimize Recursion in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare the memoization array for Fibonacci numbers.

DSA Java

int[] memo = new int[[1]];

Drag options to blanks, or click blank then click option'

An

B2 * n

Cn - 1

Dn + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of n + 1 causes ArrayIndexOutOfBoundsException.

Using n - 1 misses the last Fibonacci number.

The memo array size should be n + 1 to store Fibonacci values from 0 to n inclusive.

2fill in blank

medium

Complete the code to check if the Fibonacci value is already computed in memo.

DSA Java

if (memo[[1]] != 0) return memo[[1]];

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An + 1

Bn - 1

Cn

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Checking memo[n - 1] instead of memo[n].

Checking memo[0] which is unrelated to current n.

We check memo[n] to see if Fibonacci of n is already computed.

3fill in blank

hard

Fix the error in the recursive call to compute Fibonacci with memoization.

DSA Java

memo[n] = fib([1], memo) + fib([2], memo);

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An + 1

Bn - 1

Cn - 2

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causes infinite recursion.

Using n instead of n-1 or n-2 causes wrong results.

Fibonacci is sum of fib(n-1) and fib(n-2).

4fill in blank

hard

Fill both blanks to complete the base case and return statement in Fibonacci with memoization.

DSA Java

if (n <= [1]) return [2];

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A1

B0

Cn

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 1 for n=0 is incorrect.

Using 2 as base case limit is wrong.

Base case: if n <= 1, return n (0 or 1).

5fill in blank

hard

Fill all three blanks to complete the memoized Fibonacci function.

DSA Java

public static int fib(int n, int[] memo) {
    if (n <= [1]) return [2];
    if (memo[[3]] != 0) return memo[n];
    memo[n] = fib(n - 1, memo) + fib(n - 2, memo);
    return memo[n];
}

Drag options to blanks, or click blank then click option'

A1

Bn

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong base case values.

Checking memo with wrong index.

Base case returns n if n <= 1; check memo[n] for cached value.

Practice

1. What is the main purpose of using memoization in recursive functions?

easy

A. To store results of expensive function calls and reuse them

B. To make the code shorter and simpler

C. To avoid using loops in recursion

D. To increase the number of recursive calls

Solution

1. Step 1: Understand recursion inefficiency

   Recursive functions often repeat the same calculations multiple times, which wastes time.

2. Step 2: Role of memoization

   Memoization saves the results of these repeated calculations so they can be reused instead of recalculated.

3. Final Answer:

   To store results of expensive function calls and reuse them -> Option A

4. Quick Check:

   Memoization = Store and reuse results [OK]

Hint: Memoization saves repeated results to speed recursion [OK]

Common Mistakes:

• Thinking memoization makes code shorter
• Confusing memoization with iteration
• Believing memoization increases recursion calls

2. Which of the following Java code snippets correctly declares a memoization cache for storing integer results by input integer keys?

easy

A. Map memo = new HashMap<>();

B. List<Integer> memo = new ArrayList<>();

C. int[] memo = new int();

D. HashSet<Integer> memo = new HashSet<>();

Solution

1. Step 1: Identify suitable data structure for key-value pairs

   Memoization requires storing results by input keys, so a Map is ideal.

2. Step 2: Check Java syntax correctness

   Map memo = new HashMap<>(); uses Map with HashMap, which is correct syntax for memoization cache.

3. Final Answer:

   Map memo = new HashMap<>(); -> Option A

4. Quick Check:

   Memo cache = Map for key-value pairs [OK]

Hint: Use Map for key-value memo cache in Java [OK]

Common Mistakes:

• Using List instead of Map for memoization
• Incorrect array declaration syntax
• Using Set which stores only keys, no values

3. What will be the output of the following Java code using memoization for Fibonacci numbers?

import java.util.*;
public class FibMemo {
  static Map memo = new HashMap<>();
  public static int fib(int n) {
    if (n <= 1) return n;
    if (memo.containsKey(n)) return memo.get(n);
    int result = fib(n-1) + fib(n-2);
    memo.put(n, result);
    return result;
  }
  public static void main(String[] args) {
    System.out.println(fib(5));
  }
}

medium

A. Error at runtime

B. 8

C. 5

D. 13

Solution

1. Step 1: Understand Fibonacci sequence calculation

   fib(5) = fib(4) + fib(3), and so on, with base cases fib(0)=0, fib(1)=1.

2. Step 2: Calculate fib(5) with memoization

   fib(2)=1, fib(3)=2, fib(4)=3, fib(5)=5. Memoization avoids repeated calls but result is same.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   fib(5) = 5 [OK]

Hint: Recall Fibonacci(5) = 5, memoization doesn't change result [OK]

Common Mistakes:

• Confusing Fibonacci values for wrong n
• Assuming memoization changes output
• Thinking code causes runtime error

4. Identify the error in this Java memoized factorial function:

import java.util.*;
public class FactorialMemo {
  static Map memo = new HashMap<>();
  public static int fact(int n) {
    if (n == 0) return 1;
    if (memo.containsKey(n)) return memo.get(n);
    int result = n * fact(n - 1);
    memo.put(n, result);
    return result;
  }
  public static void main(String[] args) {
    System.out.println(fact(-1));
  }
}

medium

A. Memo map is not initialized properly

B. fact method should return long instead of int

C. Incorrect multiplication order in recursion

D. No base case for negative input causes infinite recursion

Solution

1. Step 1: Analyze base cases and input handling

   Base case handles n == 0 only, but negative n causes no stop condition.

2. Step 2: Effect of negative input

   Calling fact(-1) leads to infinite recursion because n never reaches 0 or memoized value.

3. Final Answer:

   No base case for negative input causes infinite recursion -> Option D

4. Quick Check:

   Missing negative base case = infinite recursion [OK]

Hint: Check base cases cover all input ranges [OK]

Common Mistakes:

• Ignoring negative input handling
• Assuming memo initialization error
• Thinking multiplication order causes error

5. You want to optimize a recursive function that calculates the number of ways to climb n stairs taking 1 or 2 steps at a time. Which memoization approach below correctly implements this in Java?

hard

A. Use a List<Integer> to store results; always calculate recursively without checking cache.

B. Use a Map to store results; check cache before recursive calls; store results after calculation.

C. Use an int array without initializing values; store results only after all recursion ends.

D. Use a Set<Integer> to store visited stairs; return size of set as result.

Solution

1. Step 1: Understand problem and memoization needs

   We must store number of ways for each stair number to avoid repeated calculations.

2. Step 2: Evaluate memoization approaches

   Use a Map to store results; check cache before recursive calls; store results after calculation. uses Map to store and check results before recursion, which is correct memoization practice.

3. Final Answer:

   Use a Map to store results; check cache before recursive calls; store results after calculation. -> Option B

4. Quick Check:

   Memo = Map with cache check and store [OK]

Hint: Check cache before recursion, store after calculation [OK]

Common Mistakes:

• Not checking cache before recursive calls
• Using List or Set incorrectly for memoization
• Storing results too late or not at all